Abstract

We describe a multiframe blind deconvolution (MFBD) algorithm that uses spectral ratios (the ratio of the Fourier spectra of two data frames) to model the inherent temporal signatures encoded by the observed images. In addition, by focusing on the separation of the object spectrum and system transfer functions only at spatial frequencies where the measured signal is above the noise level, we significantly reduce the number of unknowns to be determined. This “compact” MFBD yields high-quality restorations in a much shorter time than is achieved with MFBD algorithms that do not model the temporal signatures; it may also provide higher-fidelity solutions.

© 2011 Optical Society of America

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References

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  1. A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems (V. H. Winston, 1977).
  2. V. Katkovnik, K. Egiazarian, and J. Astola, in Blind Image Deconvolution: Theory and Applications, P.Campisi and K.Egiazarian, eds. (CRC Press, 2007), pp. 95–139.
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  4. N. Miura, Opt. Lett. 28, 2312 (2003).
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  5. J. G. Nagy and V. Mejia-Bustamante, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, S.Ryan, ed. (Maui Economic Development Board, 2009), pp. 99–108.
  6. D. A. Hope and S. Prasad, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, S.Ryan, ed. (Maui Economic Development Board, 2010), pp. 587–593.
  7. D. A. Hope and S. M. Jefferies, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, S.Ryan, ed. (Maui Economic Development Board, 2006), pp. 265–272.
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    [CrossRef]
  9. W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes in C, 2nd ed.(Cambridge U. Press, 1992).
  10. L. M. Mugnier, C. Robert, J.-M. Conan, V. Michau, and S. Salem, J. Opt. Soc. Am. A 18, 862 (2001).
    [CrossRef]
  11. C. L. Matson, K. Borelli, S. M. Jefferies, E. K. Hege, C. C. Beckner, and M. Lloyd-Hart, Appl. Opt. 48, A75 (2009).
    [CrossRef]

2009

2003

2001

1995

1993

S. M. Jefferies and J. C. Christou, Astrophys. J. 415, 862(1993).
[CrossRef]

Arsenin, V. Y.

A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems (V. H. Winston, 1977).

Astola, J.

V. Katkovnik, K. Egiazarian, and J. Astola, in Blind Image Deconvolution: Theory and Applications, P.Campisi and K.Egiazarian, eds. (CRC Press, 2007), pp. 95–139.
[CrossRef]

Beckner, C. C.

Borelli, K.

Christou, J. C.

S. M. Jefferies and J. C. Christou, Astrophys. J. 415, 862(1993).
[CrossRef]

Conan, J.-M.

Egiazarian, K.

V. Katkovnik, K. Egiazarian, and J. Astola, in Blind Image Deconvolution: Theory and Applications, P.Campisi and K.Egiazarian, eds. (CRC Press, 2007), pp. 95–139.
[CrossRef]

Flannery, B. P.

W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes in C, 2nd ed.(Cambridge U. Press, 1992).

Hege, E. K.

Hope, D. A.

D. A. Hope and S. Prasad, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, S.Ryan, ed. (Maui Economic Development Board, 2010), pp. 587–593.

D. A. Hope and S. M. Jefferies, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, S.Ryan, ed. (Maui Economic Development Board, 2006), pp. 265–272.

Jefferies, S. M.

C. L. Matson, K. Borelli, S. M. Jefferies, E. K. Hege, C. C. Beckner, and M. Lloyd-Hart, Appl. Opt. 48, A75 (2009).
[CrossRef]

S. M. Jefferies and J. C. Christou, Astrophys. J. 415, 862(1993).
[CrossRef]

D. A. Hope and S. M. Jefferies, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, S.Ryan, ed. (Maui Economic Development Board, 2006), pp. 265–272.

Katkovnik, V.

V. Katkovnik, K. Egiazarian, and J. Astola, in Blind Image Deconvolution: Theory and Applications, P.Campisi and K.Egiazarian, eds. (CRC Press, 2007), pp. 95–139.
[CrossRef]

Lloyd-Hart, M.

Matson, C. L.

Mejia-Bustamante, V.

J. G. Nagy and V. Mejia-Bustamante, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, S.Ryan, ed. (Maui Economic Development Board, 2009), pp. 99–108.

Michau, V.

Miura, N.

Mugnier, L. M.

Nagy, J. G.

J. G. Nagy and V. Mejia-Bustamante, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, S.Ryan, ed. (Maui Economic Development Board, 2009), pp. 99–108.

Prasad, S.

D. A. Hope and S. Prasad, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, S.Ryan, ed. (Maui Economic Development Board, 2010), pp. 587–593.

Press, W. H.

W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes in C, 2nd ed.(Cambridge U. Press, 1992).

Robert, C.

Salem, S.

Teukolsky, S. A.

W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes in C, 2nd ed.(Cambridge U. Press, 1992).

Thiébaut, E.

Tikhonov, A. N.

A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems (V. H. Winston, 1977).

Vettering, W. T.

W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes in C, 2nd ed.(Cambridge U. Press, 1992).

Appl. Opt.

Astrophys. J.

S. M. Jefferies and J. C. Christou, Astrophys. J. 415, 862(1993).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Lett.

Other

J. G. Nagy and V. Mejia-Bustamante, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, S.Ryan, ed. (Maui Economic Development Board, 2009), pp. 99–108.

D. A. Hope and S. Prasad, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, S.Ryan, ed. (Maui Economic Development Board, 2010), pp. 587–593.

D. A. Hope and S. M. Jefferies, in Proceedings of the Advanced Maui Optical and Space Surveillance Technologies Conference, S.Ryan, ed. (Maui Economic Development Board, 2006), pp. 265–272.

W. H. Press, S. A. Teukolsky, W. T. Vettering, and B. P. Flannery, Numerical Recipes in C, 2nd ed.(Cambridge U. Press, 1992).

A. N. Tikhonov and V. Y. Arsenin, Solutions of Ill-Posed Problems (V. H. Winston, 1977).

V. Katkovnik, K. Egiazarian, and J. Astola, in Blind Image Deconvolution: Theory and Applications, P.Campisi and K.Egiazarian, eds. (CRC Press, 2007), pp. 95–139.
[CrossRef]

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Figures (2)

Fig. 1
Fig. 1

The left panel shows an example data frame with Poisson noise. The other panels show the object estimates after 7800 iterations using traditional MFBD (middle) and at convergence, defined as when the change in the cost function < 10 5 , at 5600 iterations for CMFBD (right). The relative residual norm errors for the restored objects, with respect to the diffraction-limited truth object, are 0.46 and 0.16 for MFBD and CMFBD, respectively.

Fig. 2
Fig. 2

Convolution cost metric plotted as a function of wall clock time. The cost is computed over the same region of frequency space in both examples. For the traditional MFBD curve (solid curve), we use Eq. (3) with the residual multiplied by M F ( u ) ; for the CMFBD curve (dotted curve), we use the first term in Eq. (5) and the mean of the two components of the second term ( K = 2 ).

Equations (12)

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G k ( u ) = F ( u ) H k ( u ) ,
H ( u ) = B ( u ) Φ ( u ) B ( u ) Φ * ( u ) ,
ε c = k u | G k obs ( u ) G k ( u ) | 2 ,
G k obs ( u ) = F o ( u ) H k o ( u ) + N k o ( u )
ε c = k u M k ( u ) | G k obs ( u ) G k ( u ) | 2 + k j k u M j k ( u ) | G j obs ( u ) G j , k ( u ) | 2 ,
G j , k ( u ) = F ( u ) H k ( u ) [ G j obs ( u ) / G k obs ( u ) ] ,
G j , k ( u ) = F ( u ) S j ( u ) T k ( u ) ,
S j ( u ) = [ H j o ( u ) + N j o ( u ) / F o ( u ) ]
T k ( u ) = { H k o ( u ) / H k ( u ) + N k o ( u ) / [ F o ( u ) H k ( u ) ] } 1 .
ε pos = x j k s j , k 2 ( x )
ε hole = u M F ( u ) | F ( u ) | 2 ,
ε = ε c + α ( m ) ε pos + β ( n ) ε hole ,

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